{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 集成加速度计数据\n",
    "在上一课中，我给你了一个`get_derivative_from_data`函数的代码，然后让亲自尝试实现它。在这一节中，我们将对`get_integral_from_data`做类似的事情。\n",
    "\n",
    "----\n",
    "\n",
    "## 第1部分 - 重新熟悉 x(t) --> v(t) --> a(t)\n",
    "首先，请回顾一下自己上一课做了什么。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from helpers import process_data, get_derivative_from_data\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "PARALLEL_PARK_DATA = process_data(\"parallel_park.pickle\")\n",
    "\n",
    "TIMESTAMPS    = [row[0] for row in PARALLEL_PARK_DATA]\n",
    "DISPLACEMENTS = [row[1] for row in PARALLEL_PARK_DATA]\n",
    "YAW_RATES     = [row[2] for row in PARALLEL_PARK_DATA]\n",
    "ACCELERATIONS = [row[3] for row in PARALLEL_PARK_DATA]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ESXtJ+q6khZKWSfqDpGslnShp03YV0kavWj6h2v1mZlUDgqRfAh8DZgMHAVsAbwU+B6wPXC3psHYU0kavUj5hwjix/OVXPAmemVVUa6TyByPiqbL7ngf+N72cK2liy0pmDckuwfnYyAo2HZjACy+/wjPLVwKvJpmz25pZf6taQygFA0kbShqXXn+zpMMkTchuY52plE9YPONgNnzteqxctfZUUE4ym1lWnqTyzcD6koaAG4DjgB+0slDWfNWSyU4ym1lJnoCgiFhOsqDNtyPiCJJcgnURD1ozs3pyBQRJewHHAKW5lls2S6q1hgetmVk9eQLCKcAZwFURcY+kbYEbW1ssazYPWjOzeuqNQxgPHBoRh0XEVwEi4qGIOLktpbOm8qA1M6ulZkCIiFXA7m0qi7WJ8wlmVkmeJqP5kq6R9EFJR5YuLS+ZtYzzCWZWSZ7k8OuBp4H9MvcFcGVLSmQtlx20Vmn5zVI+wQPWzPpL3YAQEce1oyDWXodPG+LwaUNMnT6LqPC48wlm/aduk1E6OvkGSXent3eR9LnWF83awfkEs841c/5S9p4xp23zj+XJIVxA0u10JUBELASOamWhrH2cTzDrTDPnL+WMKxexdGQFQXt+j3kCwgYRcUfZfa+0ojDWfh6fYNZZSrWCUy9fwIqVq9Z6rNW/xzwB4SlJ25G0IiDp/cDjLSuRtZ3HJ5h1hmytoJpW/h7z9DI6ETgf2FHSUmAxyTQW1mMmDw5U/CKOk5g6fRaTBwc4/cAd3PvIrEXOmf3AOrWCcq1c5CpPQIiI2F/ShsC4iHhO0tSWlcgKc/qBO3DGlYvW+UKuiqQfktdQMGu+mfOXrlm3pFKPv6yBCeM5/cAdWlaWPE1GVwBExAsR8Vx6389aViIrTDafIGC81m1Eck7BrHnKE8e1DA0O8JUjd27pyVjVGoKkHYGdgE3LRiZvQrKE5phJOgc4FHgZ+D1wXESMNLJPa47S+ASAqdNnVdzGOQWz5sjTRDQwYXzLA0FJrRrCDsAhwCDJP+/SZTfg4w0e91fA2yJiF+BBkm6t1mE8RsGstWqdXIn21AqyqtYQIuJq4GpJe0XEbc08aERcl7l5O/D+Zu7fmqNaTgGcTzBrhmodOYYGB7hl+n4VntFaeXIIT7d4pPJHgV9We1DS8ZLmSpq7bNmyJh7W6vEYBbPWKI01WDqyYp3u3q1OHNfSspHKkq6XdHeFy/sy25xJMsjt0mr7iYjzI2I4IoYnTZqUo7jWTB6jYNZc5WMNAtb8vtrdRFQuT7fTDSLiDq3d46TuSOWI2L/W45I+TJKjeHdE1EuwW8GqVW1L+QSPTzDLp1IiOSiumSirkJHKkg4CPgMcFhHLG9mXtYfnPDJrjmq16k6obecJCCcC/8mrI5VPBf6xweN+B9gY+JWkBZL+o8H9WYs5n2DWHNV677VyBHJeedZDeAhYa6RyoweNiO0b3Ye1n9dQMBu70ojkUiI5+xsqMpGcVTcgSBoEPgRMAdYr5RIi4uSWlsw6luc8MhudUiK5lDsoJZJLuYNO+b3kSSpfSzJWYBGwurXFsW7gOY/MRqeTE8lZeQLC+hFxWstLYl0juybzYyMrGCetCQYlXpfZ7FWdnEjOyhMQfijp48AvgJdKd0bEn1pWKut4nvPILL9qzaydkEjOytPL6GXgHOA2YF56mdvKQll38ZxHZrVV6rbdKYnkrDwB4TRg+4iYEhFT08u2rS6YdQ+PUTCrrXxq+aJHJFeTp8noHsCDx6yqbE6hUrXY+QTrV9nFb7qh912egLAKWCDpRtbOIbjbqa3hMQpmayvvatoNve/yNBnNBM4GbuXVHMK8VhbKupfzCWaJSl1NO31Ef56Rype0oyDWG7yGglmiW7qaZlWtIUj6uaRDJU2o8Ni2kr4o6aOtLZ51G895ZJbo5DmLqqnVZPRx4K+A+yXdKelaSXMkLSaZ7G5eRFzcllJaV/EaCmbd09U0q9YSmk8AnwY+LWkKsAWwAnjQU1ZbHp7zyPpZ+Yj+bvi+q5vWphkeHo65cz0mrluU97KoZGDC+I7sj23WSyTNi4jhetvl6XZqNiae88j6TbeNOyjngGAt5TmPrF9047iDcnXHIUg6Jc99ZvV4jIL1sm4cd1Auz8C0D1e47yNNLof1Ac95ZL2sG8cdlKvaZCTpaODvgamSrsk8tDHwdKsLZr3Hcx5ZL+uWKa5rqZVDuBV4HJgInJu5/zlgYSsLZb3Lcx5Zr6o0Sr/Txx2UqzUO4RHgEWCv9hXH+kW1s6lSPqHbemeYdeO4g3J1exlJOhL4KrA5ybrQAiIiNmlx2ayHec4j60XZXnXdKE+3068Bh0bEfa0ujPUP5xOsV3T72IOsPL2M/uhgYK3gOY+s25XGHiwdWUHQ/b3l8gSEuZIul3S0pCNLl0YOKulLkhZKWiDpOkmTG9mfdTePT7Bu1QtjD7LyBIRNSJbQPAA4NL0c0uBxz4mIXSJiV+AXwOcb3J91MY9PsG7VC2MPsvIskHNcsw8aEc9mbm4IFXsgWp9wPsG6VS+MPcjKM3XFmyXdIOnu9PYukj7X6IElnS3pUeAYatQQJB0vaa6kucuWLWv0sNahnE+wbtSNax7UkqfJ6ALgDGAlQEQsBI6q9yRJ10u6u8Llfel+zoyIrYBLgZOq7Scizo+I4YgYnjRpUp7XZF2s2plVaQ0F5xSsk2RXCBQwNDjQ1dO55+l2ukFE3CGtde72Sr0nRcT+OctwGTAL+Jec21sPqzY+oTRttscoWKfp9rEHWXlqCE9J2o60nV/S+0mmtBgzSW/K3DwMuL+R/VnvKD/jGq91G5G6uReHWSfLU0M4ETgf2FHSUmAxcGyDx50haQdgNcn0GCc0uD/rIV5DwTpdLw1Gy8rTy+ghYH9JGwLjIuK5Rg8aEX/T6D6sP/RaLw7rfr2wEE41eXoZDUo6GfgScLak8ySd1/qimVXuxSGSH6ETzFaEXhuMlpWnyeha4HZgEUkTj1nblI9REK8OWumlMzPrHr02GC0rT0BYPyJOa3lJzKoo5RT2njFnneYjD1qzduvlZsw8vYx+KOnjkraQ9PrSpeUlMyvTy2dm1j16bTBaVp6A8DJwDnAbMC+9zG1locwq8SR41gl6bTBaliJqTyMk6ffAOyLiqfYUqbrh4eGYO9exqF+V9+4oNzBhfM/8MM2aSdK8iBiut12eHMI9JLOdmhXKk+BZUXp13EG5PAFhFbBA0o3AS6U7I+LklpXKrIpSgnnq9FkVp8h1PsGarZfHHZTLExBmphezjlGtp0dpErxePouz9qo17qDXvl95RipfImkA2Doiun/khfUET4Jn7dJPvdvyjFQ+FFgA/Hd6e1dJ17S6YGa1eBI8a5dqvdt6YdxBuTzdTs8C9gRGACJiATC1hWUyy6W0qM7iGQezukpvuV48i7P26uVxB+XyBIRXIuLPZfd5yUvrKB6jYK3Sy+MOyuVJKt8t6e+B8ek6BicDt7a2WGajUy2nAM4n2Nj0S1fTrDw1hE8AO5F0Ob0M+DNwaisLZTZa2bO4SpxPsNEodTVdOrKC4NWTil6vadYNCBGxPF3/eI/08rmIeLEdhTMbjVJOYd30csL5BMurl6e4riVPL6NfSRrM3H6dpNmtLZbZ2DmfYI3qp66mWXmajCZGxEjpRkQ8A2zeuiKZNaZSr5CSfqn6W2P6qatpVp6AsFrS1qUbkrbBvYysgzmfYI3qp66mWXl6GZ0J/FbSTentfYDjW1cks8Z5ziNrRHYixX7qZVR3+msASROBvyBZzva2oqbC9vTXNlqVVlmDZGTz6oi++aFbf8s7/XWeJiNIZjx9kqTL6Vsl7dNI4czapVo+YVVEX3UntHxmzl/K3jPmMHX6rL7sgJCnl9HHgJuB2cAX0r9ntbZYZs3hOY8sr34de5CVp4ZwCrAH8EhE7AtMA5a1tFRmTeQ5jyyPfh17kJUnILxYGogm6bURcT/QlFS7pE9JijRHYdZyHqNg1fTr2IOsPAFhSTowbSbwK0lXA481emBJWwHvAf7Q6L7M8vIYBaumX8ceZOWZuuKIiBiJiLOAfwYuAg5vwrG/CXwaj2mwNvIYBaumX8ceZFUdhyDp9RXuXpT+3Qj401gPKukwYGlE3KUKST6zVvIYBaukX8ceZNUamDaP5Oy90n/sALattWNJ1wNvrPDQmcBngQPyFFDS8aQD4bbeeus6W5vlV21d5lI+od/+GfSjSlNc3zJ9v6KLVZhcA9OaekBpZ+AGYHl615YkOYk9I+KJWs/1wDRrplI3w0prKEDSXNCrC6FY5c+/Vz/zpg5Mk3SkpG9IOldSQ/mDiFgUEZtHxJSImAIsAXarFwzMms35hP7mbqbryjMw7d+BE0jyB3cDJ0j6bqsLZtYOXkOhf7mb6bry1BDeCRwYEd+PiO8D7wXe1awCpDWFQuZGMivx+IT+426m68oTEB4AstncrYCFrSmOWTE8PqH/uJvpuvJMf70ZcJ+kO9LbewC3SboGICIOa1XhzNol2+WwUs+jUttyryUb+1G2Z9GmAxNYf8I4Rpav7MtupuXyBITPt7wUZh3A4xN6X3nPopEVKxmYMJ5vfmDXvg4EJXmajOYCv4mIm4DHgU2BWyPipvQ+s55SrQ15nNS30yL3Cvcsqi1PQLgZWF/SEMn4geOAH7SyUGZF8hoKvcs9i2rLExAUEcuBI4FvR8QRwE6tLZZZcbyGQu9yz6LacgUESXsBxwCz0vsqd8cw6xFeQ6E3uWdRbXkCwqnAGcBVEXGPpG2BG1tbLLPO4TEKvaO89jc0ONCTU1WMVd1eRmni+KbM7YeAk1tZKLNOcvqBO1Sd86iUTwD8T6WDVZrEzp/XumpNf/2tiDhV0s+psGaBxx9Yv/AYhe5W3tXUQby6WjWEH6Z/v96Ogph1Mo9R6F61upo6IKytag4hIualf28C7gXuLY098PgD61fOJ3QfdzXNr2pAUOIsSU8B9wMPSlomySOXrW95zqPu466m+dXqZXQqsDewR0RsFhGvA94B7C3pk20pnVmH8RoK3WPm/KXsPWMOS0dWrDO9ubuaVlYrIHwIODoiFpfuSHsYHZs+ZtaXvIZC5yslkkudALJrAburaXW1ksoTKq1TEBHLJE1oYZnMukK1NZlLcx65e2NxKiWSgyQY9POayfXUqiG8PMbHzPqC5zzqXE4kj02tgPB2Sc9WuDwH7NyuApp1Ks951LmcSB6bWt1Ox0fEJhUuG0eEm4zM8JxHncpzFo1NnrmMzCwHj1EoVqlX0dTpszhn9gP8ze5DnrNolPKsmGZmOXjOo+JUmp7iinlLHQRGyTUEsybxGIXieCW05nBAMGsij1EohnsVNYcDglkLuJdLe/n9bg4HBLMWqNTLRSRt204wN4+np2iuQgJCOmneUkkL0st7iyiHWauU5xPEq4uKeMBac3h6iuYrsobwzYjYNb1cW2A5zFqilE8YGhxYZw0FJzwbV296CgeD0XOTkVmLOeHZGn5fm6/IgHCSpIWSLpb0umobSTpe0lxJc5ctW9bO8pk1RbXEZmkSPOcUxsaJ5OZrWUCQdL2kuytc3gd8D9gO2BV4HDi32n4i4vyIGI6I4UmTJrWquGYt40nwmsuJ5NZp2UjliNg/z3aSLgB+0apymBWt1JZ9zuwHeGxkBeMkVpXNe+Q1fvMpH5FcSiSXcgeebrwxhUxdIWmLiHg8vXkEcHcR5TBrl8OnDa35RzV1+qyK27jtuz6vc9BaReUQviZpkaSFwL6Al+S0vuFJ8MbOieTWKqSGEBEfLOK4Zp3Ak+CNzsz5S2s2t4ETyc3ibqdmbeZJ8PLLDj4LqBgMnEhuHgcEswJ4Erx8KuUMIFmdzuscNJ/XQzAr0OTBgTVTL2SV8gn93mumWmBcHcHiGQe3uTS9zzUEswJVG6MA/T0+oTTWoPKipM4ZtIoDglmBnE9YV/mkdeWcM2gdBwSzgtXLJ/TblNnV8gbgnEGrOYdg1iGq5ROgv7qjVssbCDz4rMVcQzDrELXyCdD7zUfOGxTPNQSzDpGd86haTaFXu6OWz1FUznmD9nANwayDZBfVqaRXp8x23qAzOCCYdaB+mTI7O5V1JaW8gYNBezggmHWgbHdUkYzMLdftOYVjNm1IAAAJIUlEQVR63UvBeYN2c0Aw61Cl5qPFMw5mdYU5fKC7u6TWaiYC5w2K4KSyWRfolS6p2ZlLq/UmAi92UxTXEMy6QJ4uqadevqCjawvlM5dWU1rsxsGg/VxDMOsCebqkQmfWFkq1glrlLnEzUbEUVdomO9Hw8HDMnTu36GKYFapWr5yS8RKrI5hccNNLvfEFJYLCy9rLJM2LiOF627mGYNZlaq24VlJaSKaoGsNoagVeD7lzOIdg1mXqzZBart35hTzdSUvcRNRZXEMw60KHTxvi8GlDuZtkoLW1hTzrHpdzT6LO4xyCWZcr6p9xtllIULPnUNbAhPGeiqLN8uYQHBDMeshoagwTxomN1l+PkeUr2XRgAhI1r08eHGDfHSdx4/3LRh0ESlwrKIaTymZ9KG/3VICVq4Nnlq8EYGTFyjX3V7u+dGQFP7r9D2tujyYYuFbQHZxUNusxpSkvvvWBXWsOZmu18RLCs5V2k8JqCJI+AZwEvALMiohPF1UWs140mtpCs7lG0J0KCQiS9gXeB+wSES9J2ryIcpj1urH0RhqrUk7BeYLuVVQN4R+BGRHxEkBEPFlQOcz6Qra28NjICjYdmMALL7/CylWNdSpxEOgthfQykrQAuBo4CHgR+FRE3Fll2+OB4wG23nrr3R955JG2ldOsl2W7q462l9FjIys81UQXKbzbqaTrgTdWeOhM4GxgDnAKsAdwObBt1CmMu52amY1e4d1OI2L/ao9J+kfgyjQA3CFpNTARWNaq8piZWW1FdTudCewHIOnNwGuApwoqi5mZUVxS+WLgYkl3Ay8DH67XXGRmZq1VSECIiJeBY4s4tpmZVeaRymZmBjggmJlZqqtmO5W0DGhkIMJEeit53WuvB/yaukWvvaZeez2w9mvaJiIm1XtCVwWERkmam6cvbrfotdcDfk3dotdeU6+9Hhjba3KTkZmZAQ4IZmaW6reAcH7RBWiyXns94NfULXrtNfXa64ExvKa+yiGYmVl1/VZDMDOzKhwQzMwM6JOAIOkgSQ9I+p2k6UWXp1GSLpb0ZDoXVE+QtJWkGyXdJ+keSacUXaZGSVpf0h2S7kpf0xeKLlMzSBovab6kXxRdlmaQ9LCkRZIWSOqJ+fUlDUr6maT709/UXrme1+s5BEnjgQeB9wBLgDuBoyPi3kIL1gBJ+wDPA/83It5WdHmaQdIWwBYR8b+SNgbmAYd3+eckYMOIeF7SBOC3wCkRcXvBRWuIpNOAYWCTiDik6PI0StLDwHBE9MzANEmXAL+JiAslvQbYICJG6j2vH2oIewK/i4iH0kn1fkKynnPXioibgT8VXY5miojHI+J/0+vPAfcBXb0UVySeT29OSC9dfQYmaUvgYODCostilUnaBNgHuAiSyUTzBAPoj4AwBDyaub2ELv9H0+skTQGmAf9TbEkalzavLACeBH4VEd3+mr4FfBpYXXRBmiiA6yTNS5fs7Xbbkiw29v20ae9CSRvmeWI/BARVuK+rz9J6maSNgCuAUyPi2aLL06iIWBURuwJbAntK6tomPkmHAE9GxLyiy9Jke0fEbsBfAyemTbLdbD1gN+B7ETENeAHIlTvth4CwBNgqc3tL4LGCymI1pO3sVwCXRsSVRZenmdIq+6+BgwouSiP2Bg5L29x/Auwn6UfFFqlxEfFY+vdJ4CqSZuZutgRYkqmN/owkQNTVDwHhTuBNkqamyZWjgGsKLpOVSROwFwH3RcQ3ii5PM0iaJGkwvT4A7A/cX2ypxi4izoiILSNiCsnvaE5EdPVCV5I2TDsxkDarHAB0de+9iHgCeFTSDuld7wZydc4oagnNtomIVySdBMwGxgMXR8Q9BRerIZJ+DLwLmChpCfAvEXFRsaVq2N7AB4FFaZs7wGcj4toCy9SoLYBL0p5u44CfRkRPdNXsIW8ArkrOR1gPuCwi/rvYIjXFJ4BL05Pgh4Dj8jyp57udmplZPv3QZGRmZjk4IJiZGeCAYGZmKQcEMzMDHBDMzCzlgGBdRdJm6ayUCyQ9IWlp5vatLTrmNEkdM3ePpB9Ien+Nx0+SlKuboVlWz49DsN4SEU8DuwJIOgt4PiK+3uLDfhb4couP0UwXA7cA3y+6INZdXEOwniHp+fTvuyTdJOmnkh6UNEPSMenaBIskbZduN0nSFZLuTC97V9jnxsAuEXFXevudmRrJ/Mwo19PTfSzMrnsg6UPpfXdJ+mF63zaSbkjvv0HS1un9P5B0nqRbJT1UqgUo8R1J90qaBWye2f+M9P6Fkr4OEBHLgYcldfsUDNZmriFYr3o78BaSacIfAi6MiD2VLLzzCeBU4N+Ab0bEb9N/yrPT52QNs/ZUBp8CToyIW9KJ+F6UdADwJpI5cARck06Q9jRwJsnkaU9Jen26j++QrGVxiaSPAucBh6ePbQH8JbAjyRQrPwOOAHYAdiYZWXsvcHG6vyOAHSMiStNkpOYCfwXcMZY3z/qTA4L1qjsj4nEASb8HrkvvXwTsm17fH3hrOm0BwCaSNk7XYyjZgmQq4ZJbgG9IuhS4MiKWpAHhAGB+us1GJAHi7cDPSguvRERpDYu9gCPT6z8EvpbZ/8yIWA3cK+kN6X37AD+OiFXAY5LmpPc/C7wIXJjWHLLTYjxJElTMcnOTkfWqlzLXV2dur+bVE6FxwF4RsWt6GSoLBgArgPVLNyJiBvAxYAC4XdKOJLWCr2T2s306t5TIN9V6dptsuVVlm1JZXiGplVxBUsPIzsGzflp2s9wcEKyfXQecVLohadcK29wHbJ/ZZruIWBQRXyVpltmRpKnpo2kTEpKGJG0O3AD8naTN0vtLTUa3kswWCnAMydKatdwMHJUutrMFaQ0nPd6m6QSAp5Im21Nvpstn7bT2c5OR9bOTge9KWkjyW7gZOCG7QUTcL2nTTFPSqZL2BVaRtOX/MiJekvQW4La0+el54NiIuEfS2cBNklaRNCl9JD3uxZJOJ2mOqtdF9CpgP5LmrgeBm9L7NwaulrQ+SW3ik5nn7A18AbNR8GynZnVI+iTwXER0zFiEWiRNA06LiA8WXRbrLm4yMqvve6zdtt/pJgL/XHQhrPu4hmBmZoBrCGZmlnJAMDMzwAHBzMxSDghmZgY4IJiZWer/A7hfI5QF84E4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You saw this plot of displacement versus time.\n",
    "\n",
    "plt.title(\"Displacement vs Time while Parallel Parking\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Displacement (meters)\")\n",
    "plt.scatter(TIMESTAMPS, DISPLACEMENTS)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and you saw how you could differentiate this data\n",
    "# to get velocity vs time\n",
    "\n",
    "speeds = get_derivative_from_data(DISPLACEMENTS, TIMESTAMPS)\n",
    "\n",
    "plt.title(\"Speed vs Time while Parallel Parking\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Speed (m / s)\")\n",
    "plt.scatter(TIMESTAMPS[1:], speeds)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# AND you saw how you could differentiate velocity data\n",
    "# to get acceleration data...\n",
    "\n",
    "accels = get_derivative_from_data(speeds, TIMESTAMPS[1:])\n",
    "\n",
    "plt.title(\"Acceleration vs Time while Parallel Parking\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Acceleration (m / s / s)\")\n",
    "plt.scatter(TIMESTAMPS[2:], accels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第2部分 - 其他方式: a(t) --> v(t) --> x(t)\n",
    "现在我们将使用积分从加速度数据返回到位置数据。首先，我们将原始加速度计数据绘制成图，然后将其与该单元格上方的图形进行比较。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9Pp21HAH8uJ4FzJrRxZzDdqars4KArs5K0xuW6mng+nVWOth8445X1vWoPaYOOm6o7qLz1Hu6do+h6Dzttn+2o+H85lptexa66knS4oiYIemjwLYR8SlJ90XELg0LTHov8BWyy2Mvioizh5p2JFc9mZmNd0Wveip6H8X6krYGDgfOHFVkBUXET4CfjEVZZmY2tKKXt34GWEB2yerdkt4A/E/jwjIzs7IodEYRET8AflDV/zDwV40KyszMysPPejIzs1xOFGZmlqvWndl7Shrs5jczMxsnap1RHAMsknSFpGMlbTUWQZmZWXnkNmZHxIkAknYEDgYukbQZcDNwHXB7RPjJc2ZmbaxQG0VELIuIL0fEQcB+wG3A3wB3NjI4MzNrvmG/uCgi+shuhPPNcGZm44CvejIzs1xOFGZmlqvo02M36X+bnaQ3STpUUkdjQzMzszIoekZxK7CRpC7gRuA44JJGBWVmZuVRNFEoIp4HDgO+HhEfBHZqXFhmZlYWhROFpD2BDwPXpmHDvmLKzMxaT9FEcQpwBnB1RDyQHjN+c+PCMjOzsij6mPFbydop+vsfBv6pUUGZmVl5+PJYMzPL5URhZma5aj1m/EhJW4xVMGZmVj612ii2A36Qbq67Efhv4K6IiIZHZmZmpVDrMePnAOdImggcABwPfEvSg2SPGV8QEb9vfJiNd83ilcxdsJxVvX1sVulAgt7n1zCls8K+O07m5mU964xr5HT1WPaUzgqzZ05n1oyuZn+9ZtbCNJKTA0k7kb2f4sCImFnXgKS5wPuB1cBvgOMiojdvnu7u7li4cOGIy7xm8UrOmL+EvjXt92qNSscE5hy2s5OFma1D0qKI6K413YgasyNiaUR8qd5JIvkp8NaI2AX4Ndn9Gw01d8HytkwSAH1r1jJ3wfJmh2FmLax0Vz1FxPUR8VLqvQPYptFlrurta3QRTdXu62dmjVW6RDHA8WQN6OuQdIKkhZIW9vT0jKqQKZ2VUc1fdu2+fmbWWIUThaTNJe0i6W39n5EWKukGSfcP8vlA1TRnAi8Blw+2jIiYFxHdEdE9efLkkYYCwOyZ06l0TBjVMsqq0jGB2TOnNzsMM2thhR7hIemzwLFkjcv9rd9B9v7sYYuIA2qUdwxwCLD/WFyK29/Q66uezMzWVfQJsIcD20fE6kYGAyDpIODjwD7p0eZjYtaMLv9DNTMbRNGqp/uBzkYGUuU8YCLwU0n3SPrWGJVrZmaDKHpGMQdYLOl+4MX+gRFxaL0Diogd6r1MMzMbuaKJ4lLg88AS4OXGhWNmZmVTNFE8FRFfa2gkZmZWSkUTxSJJc4Af8+qqp181JCozMyuNooliRvq7R9WwEV8ea2ZmraPoq1D3bXQgZmZWTrVeXHSUpCGnkbS9pL3rH5aZmZVFrTOKLcgui10ELAJ6gI2AHYB9gKeATzQ0QjMza6paLy76qqTzyNoi9gJ2AfqAB4GPRMTvGh+imZk1U802iohYS/aOiJ82PhwzMyubsj9m3MzMmsyJwszMcjlRmJlZrqLvo9gQ+CtgWvU8EfGZxoRlZmZlUfTO7B8B/0t2ieyLNaY1M7M2UjRRbBMRBzU0EjMzK6WibRS/kLRzQyMxM7NSKnpGsTdwrKRHyKqeBERE7NKwyMzMrBSKJoqDGxqFmZmVVqGqp4j4Ldk7s9+fPp1pmJmZtblCiULSKcDlwGvT5zJJJzcyMDMzK4eiVU9/C/xlRDwHIOnzwC+BrzcqMDMzK4eiVz0JWFvVvzYNMzOzNlf0jOJi4E5JV6f+WcCFjQkpI+l0YC4wOSKeamRZZmY2tKKvQj1X0i1kl8kKOC4iFjcqKEnbAu8B/L4LM7Mmy00UkiZFxNOSXgM8mj79414TEX9sUFxfBv6V7NEhZmbWRLXOKL4LHEL2jKeoGq7U/4Z6ByTpUGBlRNwrDd0MIukE4ASAqVOn1jsMMzNLar0K9ZD09/X1LFTSDcBWg4w6E/gkcGCtZUTEPGAeQHd3d9SY3MzMRqjoY8ZvjIj9aw0rKiIOGKKcnYHXA/1nE9sAv5K0e0Q8MZKyzMxsdGq1UWwEbAxsKWlz/nxJ7CRgSr2DiYglZDf09Zf/KNDtq57MzJqn1hnF3wOnkiWFRfw5UTwNfKOBcZmZWUnUaqP4KvBVSSdHxJjfhR0R08a6TDMze7Wi91F8XdJbgZ2AjaqGf6dRgZmZWTkUbcz+FPBuskTxE7LHjt8GOFGYmbW5os96+mtgf+CJiDgO2BXYsGFRmZlZaRRNFH0R8TLwkqRJwJM04GY7MzMrn6IPBVwoqRM4n+zqp2eBuxoWlZmZlUbNRKHszrc5EdELfEvSdcCkiLiv4dGZmVnT1ax6iogArqnqf9RJwsxs/CjaRnGHpL9oaCRmZlZKRdso9gVOTI/UeI709NiI2KVRgZmZWTkUTRQHNzQKMzMrrUJVTxHxW2BbYL/U/XzRec3MrLUV+mef7sz+OHBGGtQBXNaooMzMrDyKnhV8EDiUrH2CiFgFTGxUUGZmVh5FE8XqdJlsAEjapHEhmZlZmRRNFFdK+jbQKenvgBvI7tI2M7M2V/Qx41+U9B6yFxZNB/4tIn7a0MjMzKwUil4eS0oMTg5mZuNMrXdmP0Nqlxg4iuyGu0kNicrMzEqj1qtQfWWTmdk4V/imOUl7SzoudW8p6fWNC8vMzMpipDfcbYBvuDMzGxd8w52ZmeUq5Q13kk6WtFzSA5K+0MiyzMwsX9HLYwfecHc8DbrhTtK+wAeAXSLiRUmvbUQ5ZmZWTBlvuPsH4JyIeDGV/WSDyjEzswIKJYp0hdPP+5ODpIqkaRHxaANiehPwTklnAy8Ap0fE3YPEdAJwAsDUqVMbEIaZmUHxqqcfAO+o6l+bho3o9aiSbgC2GmTUmSmmzYE90vKvlPSG1EbyioiYB8wD6O7uHuymQDMzq4OiiWL9iFjd3xMRqyVtMNJCI+KAocZJ+gdgfkoMd0l6GdgS6BlpeWZmNnJFr3rqkXRof4+kDwBPNSYkrgH2S+W8ieyejUaVZWZmNRQ9ozgRuFzSeal/BXB0Y0LiIuAiSfcDq4FjBlY7mZnZ2Cl61dNvgD0kbQooIp5pVECpiuuoRi3fzMyGp+gjPP5dUmdEPBsRz0jaXNLnGh2cmZk1X9E2ioMjore/JyL+BLy3MSGZmVmZFE0UEyRt2N8jqQJsmDO9mZm1iaKN2ZcBN0q6mOx5T8cD32lYVGZmVhpFG7O/IOk+4ACyt9t9NiIWNDQyMzMrheG8M/s64DoASXtJ+kZEfKxhkZmZWSkUThSSdgOOBD4EPALMb1RQZmZWHrmJIt0ZfQRZgvgD8H2y+yj2HYPYzMysBGqdUSwDfg68PyIeApB0WsOjMjOz0qh1eexfAU8AN0s6X9L+ZI3ZZmY2TuQmioi4OiI+BOwI3AKcBrxO0jclHTgG8ZmZWZMVuuEuIp6LiMsj4hBgG+Ae4BMNjczMzEqh6J3Zr4iIP0bEtyNiv0YEZGZm5TLsRGFmZuOLE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5nCjMzCxX6RKFpN0k3SHpHkkLJe3e7JjMzMaz0iUK4AvApyNiN+DfUr+ZmTVJGRNFAJNS92bAqibGYmY27hV+FeoYOhVYIOmLZInsHYNNJOkE4ASAqVOnjl10ZmbjTFMShaQbgK0GGXUmsD9wWkRcJelw4ELggIETRsQ8YB5Ad3d3NDBcM7NxrSmJIiLW+cffT9J3gFNS7w+AC8YkKDMzG1QZ2yhWAfuk7v2A/2liLGZm414Z2yj+DviqpPWBF0jtEGZm1hylSxQRcRvw9mbHYWZmmTJWPZmZWYk4UZiZWS4nCjMzy+VEYWZmuZwozMwslxOFmZnlcqIwM7NcThRmZpbLicLMzHI5UZiZWS4nCjMzy+VEYWZmuZwozMwslxOFmZnlcqIwM7NcThRmZpbLicLMzHI5UZiZWS4nCjMzy1W6d2abmbW7axavZO6C5azq7WOzSgcS9D6/5lXdUzor7LvjZG5e1lNzutkzpzNrRlfD4nWiMDMbQ9csXskZ85fQt2YtAL19a14ZV929srePy+743aDjBk53xvwlAA1LFq56MjMbQ3MXLH8lSdRL35q1zF2wvK7LrNaURCHpbyQ9IOllSd0Dxp0h6SFJyyXNbEZ8ZmaNsqq3r6WWC807o7gfOAy4tXqgpJ2AI4C3AAcB/yFpwtiHZ2bWGFM6Ky21XGhSooiIByNisPOkDwBXRMSLEfEI8BCw+9hGZ2bWOLNnTqfSUd/j30rHBGbPnF7XZVYrWxtFF/BYVf+KNGwdkk6QtFDSwp6enjEJzsxstGbN6GLOYTvT1VlBQGelg8037linu6uzwlF7TC003ZzDdm7Nq54k3QBsNcioMyPiR0PNNsiwGGzCiJgHzAPo7u4edBozszKaNaOrof/Y661hiSIiDhjBbCuAbav6twFW1SciMzMbibJVPf0YOELShpJeD7wRuKvJMZmZjWvNujz2g5JWAHsC10paABARDwBXAkuB64CPRUR9Lzg2M7Nhacqd2RFxNXD1EOPOBs4e24jMzGwoZat6MjOzklFE618wJKkH+O0oFrEl8FSdwimLdlundlsf8Dq1inZep+0iYnKtidsiUYyWpIUR0V17ytbRbuvUbusDXqdW4XVy1ZOZmdXgRGFmZrmcKDLzmh1AA7TbOrXb+oDXqVWM+3VyG4WZmeXyGYWZmeVyojAzs1zjOlFIOii9Se8hSZ9odjz1IOkiSU9Kur/ZsdSDpG0l3SzpwfRWxFOaHdNoSdpI0l2S7k3r9Olmx1QPkiZIWizpv5odSz1IelTSEkn3SFrY7HjqQVKnpB9KWpZ+U3sWmm+8tlGkN+f9GngP2VNr7waOjIilTQ1slCS9C3gW+E5EvLXZ8YyWpK2BrSPiV5ImAouAWa28nSQJ2CQinpXUAdwGnBIRdzQ5tFGR9M9ANzApIg5pdjyjJelRoDsi2uZmO0mXAj+PiAskbQBsHBG9teYbz2cUuwMPRcTDEbEauILsDXstLSJuBf7Y7DjqJSIej4hfpe5ngAcZ4mVWrSIyz6bejvRp6SM2SdsA7wMuaHYsNjhJk4B3ARcCRMTqIkkCxneiKPw2PSsHSdOAGcCdzY1k9FI1zT3Ak8BPI6LV1+krwL8CLzc7kDoK4HpJiySd0Oxg6uANQA9wcaoivEDSJkVmHM+JovDb9Kz5JG0KXAWcGhFPNzue0YqItRGxG9nLuXaX1LLVhJIOAZ6MiEXNjqXO9oqItwEHAx9L1bqtbH3gbcA3I2IG8BxQqG12PCcKv02vRaR6/KuAyyNifrPjqad06n8LcFCTQxmNvYBDU53+FcB+ki5rbkijFxGr0t8nyV6LsHtzIxq1FcCKqrPXH5IljprGc6K4G3ijpNenRp0jyN6wZyWSGn4vBB6MiHObHU89SJosqTN1V4ADgGXNjWrkIuKMiNgmIqaR/Y5uioijmhzWqEjaJF08QaqeORBo6SsJI+IJ4DFJ09Og/cleEldTU15cVAYR8ZKkk4AFwATgovSGvZYm6XvAu4Et01sEPxURFzY3qlHZC/gIsCTV6QN8MiJ+0sSYRmtr4NJ05d16wJUR0RaXlLaR1wFXZ8cprA98NyKua25IdXEycHk6OH4YOK7ITOP28lgzMytmPFc9mZlZAU4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFtQdIW6Smf90h6QtLKqv5fNKjMGZJK82wjSZdI+uuc8SdJKnQ5pFm1cXsfhbWXiPgDsBuApLOAZyPiiw0u9pPA5xpcRj1dBNwOXNzsQKy1+IzC2p6kZ9Pfd0v6maQrJf1a0jmSPpzeDbFE0vZpusmSrpJ0d/rsNcgyJwK7RMS9qX+fqjOYxVV39c5Oy7iv+r0Tko5Ow+6V9J9p2HaSbkzDb5Q0NQ2/RNLXJP1C0sP9Zw3KnCdpqaRrgddWLf+cNPw+SV8EiIjngUcltfqjKGyM+YzCxptdgTeTPYr9YeCCiNhd2QuRTgZOBb4KfDkibkv/rBekeap18+pHOpwOfCwibk8PMHxB0oHAG8meESTgx+nBcn8AziR76NxTkl6TlnEe2XtELpV0PPAKlaFXAAACI0lEQVQ1YFYatzWwN7Aj2aNmfgh8EJgO7Ex2J/FS4KK0vA8CO0ZE9D8uJFkIvBO4ayRfno1PThQ23twdEY8DSPoNcH0avgTYN3UfAOyUHt8AMEnSxPQ+jH5bkz2yud/twLmSLgfmR8SKlCgOBBanaTYlSxy7Aj/sfyFORPS/P2RP4LDU/Z/AF6qWf01EvAwslfS6NOxdwPciYi2wStJNafjTwAvABelMo/rxIE+SJRuzwlz1ZOPNi1XdL1f1v8yfD5zWA/aMiN3Sp2tAkgDoAzbq74mIc4CPAhXgDkk7kp1FzKlazg7puVui2CPtq6epjltDTNMfy0tkZzFXkZ2RVD+jaKMUu1lhThRm67oeOKm/R9Jug0zzILBD1TTbR8SSiPg8WfXOjmRVVsenqigkdUl6LXAjcLikLdLw/qqnX5A9fRXgw2SvSM1zK3BEegnS1qQzolTeZunBiaeSGvmTN9HiT0G1seeqJ7N1/RPwDUn3kf1GbgVOrJ4gIpZJ2qyqSupUSfsCa8naCv47Il6U9Gbgl6ka61ngqIh4QNLZwM8krSWrmjo2lXuRpNlk1Vq1LmW9GtiPrNrs18DP0vCJwI8kbUR29nFa1Tx7AZ/GbBj89FizEZJ0GvBMRJTmXoo8kmYA/xwRH2l2LNZaXPVkNnLf5NVtB2W3JfB/mx2EtR6fUZiZWS6fUZiZWS4nCjMzy+VEYWZmuZwozMwslxOFmZnl+v+WXGNwVKrsBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Acceleration vs Time while Parallel Parking\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Acceleration (m / s / s)\")\n",
    "plt.scatter(TIMESTAMPS, ACCELERATIONS)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正如你所看到的，它们看起来几乎完全相同......不过有一些缺失的数据，在这个时间窗开始附近的分化步骤中丢失了。\n",
    "\n",
    "现在我将向你展示一个`get_integral_from_data`函数。仔细阅读该代码并尝试理解它，因为在稍后的notebook中，你将需要尝试亲自去实现它（如果可能，不必再回头看）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_integral_from_data(acceleration_data, times):\n",
    "    # 1. We will need to keep track of the total accumulated speed\n",
    "    accumulated_speed = 0.0\n",
    "    \n",
    "    # 2. The next lines should look familiar from the derivative code\n",
    "    last_time = times[0]\n",
    "    speeds = []\n",
    "    \n",
    "    # 3. Once again, we lose some data because we have to start\n",
    "    #    at i=1 instead of i=0.\n",
    "    for i in range(1, len(times)):\n",
    "        \n",
    "        # 4. Get the numbers for this index i\n",
    "        acceleration = acceleration_data[i]\n",
    "        time = times[i]\n",
    "        \n",
    "        # 5. Calculate delta t\n",
    "        delta_t = time - last_time\n",
    "        \n",
    "        # 6. This is an important step! This is where we approximate\n",
    "        #    the area under the curve using a rectangle w/ width of\n",
    "        #    delta_t.\n",
    "        delta_v = acceleration * delta_t\n",
    "        \n",
    "        # 7. The actual speed now is whatever the speed was before\n",
    "        #    plus the new change in speed.\n",
    "        accumulated_speed += delta_v\n",
    "        \n",
    "        # 8. append to speeds and update last_time\n",
    "        speeds.append(accumulated_speed)\n",
    "        last_time = time\n",
    "    return speeds\n",
    "\n",
    "# 9. Now we use the function we just defined\n",
    "integrated_speeds = get_integral_from_data(ACCELERATIONS, TIMESTAMPS)\n",
    "\n",
    "# 10. Plot\n",
    "plt.scatter(TIMESTAMPS[1:], integrated_speeds)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这张图看起来很熟悉吗？向上滚动并将其与来自 **区分**位置与时间的图形进行比较。它看起来与我们通过**集成**加速度与时间所做的图表有多相似？\n",
    "\n",
    "#### 代码演练\n",
    "\n",
    "**1 -** 我们将对很多小矩形的面积进行求和。这些小矩形中的每一个都将对累积总面积（表示积分加速度数据时的速度）有影响。\n",
    "\n",
    "**2 - 5 -** 这部分应该看起来很熟悉。你在`get_derivative_from_data`函数中看到过类似的代码\n",
    "\n",
    "**6 -** 这个$\\Delta v$ 是我们在循环迭代中计算的任何矩形一个面积的一小部分\n",
    "\n",
    "**7 -** 我们把这个$\\Delta v$加到总的累积速度上\n",
    "\n",
    "**8 - 10 -** 这部分应该看起来很熟悉"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Integrate AGAIN! Let's see what happens when we integrate \n",
    "# again to get displacement data...\n",
    "\n",
    "integrated_displacements = get_integral_from_data(integrated_speeds, \n",
    "                                                 TIMESTAMPS[1:])\n",
    "plt.scatter(TIMESTAMPS[2:], integrated_displacements)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 请牢记：\n",
    "\n",
    "再一次提醒你，不要试图记住这段代码！关键要记住的是：\n",
    "\n",
    "> 通过计算许多小矩形的面积并将它们相加，积分可以用来累积变化。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
